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On the Multiplicities of Characters in Table Algebras

Published online by Cambridge University Press:  20 November 2018

J. Bagherian
J. Bagherian*
Affiliation:
Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran e-mail: [email protected]
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Abstract

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In this paper we show that every module of a table algebra can be considered as a faithful module of some quotient table algebra. Also we prove that every faithful module of a table algebra determines a closed subset that is a cyclic group. As a main result we give some information about multiplicities of characters in table algebras.

Keywords

20C9916G30table algebrafaithful modulemultiplicity of character
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 2 , 14 June 2014 , pp. 231 - 239
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

This research was partially supported by the Center of Excellence for Mathematics, University of Isfahan.

References

[1] Arad, Z., Fisman, E., and Muzychuk, M., Generalized table algebras. Israel J. Math. 114 (1999), 29–60. http://dx.doi.org/10.1007/BF02785571 CrossRefGoogle Scholar
[2] Bagherian, J. and Rahnamai Barghi, A., Burnside-Brauer theorem for table algebras. Electron. J. Combin. 18(2011), P204.Google Scholar
[3] Blau, H. I., Quotient structures in C-algebras. J. Algebra 177(1995), no. 1, 297–337. http://dx.doi.org/10.1006/jabr.1995.1300 CrossRefGoogle Scholar
[4] Blau, H. I. and Zieschang, P.-H., Sylow theory for table algebras, fusion rule algebras, and hypergroups. J. Algebra 273(2004), no. 2, 551–570. http://dx.doi.org/10.1016/j.jalgebra.2003.09.041 CrossRefGoogle Scholar
[5] Isaacs, I. M., Character theory of finite groups. Pure and Applied Mathematics, 69, Academic Press [Harcourt Brace Jovanovich Publishers], New York-London, 1976.Google Scholar
[6] Hanaki, A., Faithful representation of association schemes Proc. Amer. Math. Soc. 139(2011), no. 9, 3191–3193. http://dx.doi.org/10.1090/S0002-9939-2011-11026-8 CrossRefGoogle Scholar
[7] Rahnamai Barghi, A. and Bagherian, J., Standard character condition for table algebras.Electron. J. Combin. 17(2010), no. 1, R13.Google Scholar
[8] Xu, B., Characters of table algebras and applications to association schemes. J. Combin. Theory Ser. A 115(2008), no. 8, 1358–1373. http://dx.doi.org/10.1016/j.jcta.2008.02.005 CrossRefGoogle Scholar